In this paper, we study the gravitational collapse of a spherical symmetric star constituted of matter interacting with vacuum energy density Λ in the background of spacetime curvature. We consider the gravitational collapse for closed, flat, and hyperbolic spacetime geometry (k = 1, 0,−1). We take the process of gravitational collapse for an anisotropic fluid interacting with a growing vacuum energy density by taking a complete physically general-relativistic approach in the background of spacetime curvature. Here, we achieved analytic solutions with some assumptions of physical significance. We executed and interpreted the solutions for several cases of the equation of state parameters, (l,ω). In all physical cases, we investigate the formation of a black hole and the naked singularity.

中文翻译：

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各向异性流体的引力坍缩和相互作用的真空能量密度：曲率效应

在本文中，我们研究了由与真空能量密度相互作用的物质构成的球对称恒星的引力坍缩。Λ在时空曲率的背景下。我们考虑闭合、平坦和双曲时空几何的引力坍缩(ķ = 1, 0,-1). 我们通过在时空曲率的背景下采用完整的物理广义相对论方法来研究各向异性流体与不断增长的真空能量密度相互作用的引力坍缩过程。在这里，我们通过一些具有物理意义的假设实现了解析解。我们执行并解释了状态参数方程的几种情况的解，(l,ω). 在所有物理案例中，我们都会研究黑洞的形成和裸奇点。